As of posting this guide there are 816 unique troops available in the game. Typically there are 3-5 added each week. You need 500 different troops for this achievement to unlock. You can obtain troops in many ways:
Chests - Gold are the cheapest, but only return Common/Uncommon base rarity troops. Guild, Glory, Gem and VIP chest all return various rarities.
Completing Kingdom quests rewards troops, including specific ones when finished.
Opening Chaos Portals in the Underworld (Delves)
"Buying" the latest troops for weekly eventns, using gems in the shop tab of said event can help getting a specific troop, but is ineffective at growing your total number.
Through the Soulforge, summoning stones produce 1-3 of 4 specific troops and these rotate weekly.
Only about 40 of the 800+ are mythic troops, which are incredibly hard to get randomly and are more effectively crafted through the soulforge.